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Консультация № 191662
03.11.2017, 21:19
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Здравствуйте! У меня возникли сложности с таким вопросом:
задача 9.6 диск вращается с угловой скоростью в зависимости от времени которая задается графиком. найти угол поворота диска (в радианах) за t=4c, если w max=2c^-1
а) 5 рад, б) 4 рад, в) 3 рад, г) 2 рад, д) 1 рад
задача 9.6 диск вращается с угловой скоростью в зависимости от времени которая задается графиком. найти угол поворота диска (в радианах) за t=4c, если w max=2c^-1
а) 5 рад, б) 4 рад, в) 3 рад, г) 2 рад, д) 1 рад
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Обсуждение
04.11.2017, 02:56
общий
это ответ
Здравствуйте, Tata1207!
Уравнение вращательного движения, аналогично уравнению поступательного и имеет вид
где [$966$] - угол поворота, [$969$][sub]0[/sub] - начальная угловая скорость, [$949$] - угловое ускорение, равное
В данном случае за первые 2 секунды угловая скорость изменилась от [$969$][sub]0[/sub] = 0 до [$969$][sub]max[/sub] = 2 с[sup]-1[/sup], поэтому угловое ускорение на этом отрезке времени составит
и уравнение движения примет вид
Угол поворота за первые 2 с будет равен
За следующие 2 секунды угловая скорость изменилась от [$969$][sub]0[/sub] = [$969$][sub]max[/sub] = 2 c до -[$969$][sub]max[/sub] = -2 с[sup]-1[/sup], поэтому угловое ускорение на этом отрезке времени составит
и уравнение движения примет вид
Угол поворота за следующие 2 с будет равен
Таким образом, за 4 с угол поворота диска составит 2 + 0 = 2 рад, то есть правильный ответ - г).
Уравнение вращательного движения, аналогично уравнению поступательного и имеет вид
где [$966$] - угол поворота, [$969$][sub]0[/sub] - начальная угловая скорость, [$949$] - угловое ускорение, равное
В данном случае за первые 2 секунды угловая скорость изменилась от [$969$][sub]0[/sub] = 0 до [$969$][sub]max[/sub] = 2 с[sup]-1[/sup], поэтому угловое ускорение на этом отрезке времени составит
и уравнение движения примет вид
Угол поворота за первые 2 с будет равен
За следующие 2 секунды угловая скорость изменилась от [$969$][sub]0[/sub] = [$969$][sub]max[/sub] = 2 c до -[$969$][sub]max[/sub] = -2 с[sup]-1[/sup], поэтому угловое ускорение на этом отрезке времени составит
и уравнение движения примет вид
Угол поворота за следующие 2 с будет равен
Таким образом, за 4 с угол поворота диска составит 2 + 0 = 2 рад, то есть правильный ответ - г).
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